Question

Consider the given function.

h(X) = (x+1)^2 - 4


Plot the x-intercept(s), y-intercept, vertex, and axis of symmetry of the function.

Answer 1

Explanation:

To find the intercept with the x axis, we make h (x) = 0.

0 = (x + 1) ^ 2 - 4

0 = x ^ 2 + 2x + 1 -4

0 = x ^ 2 + 2x - 3

0 = (x +3) (x-1)

x = 1

x = -3

To find the intercept with the y axis, we make x = 0.

y = (0+1)^2 -4

y = -3

For a quadratic equation of the form ax ^2 + bx+ c

The vertex is calculated with the formula x = -b/2a

So:

x = -2/2(1)

x = -1

Finally the axis of symmetry of a quadratic function always passes through the vertex.

So:

x = -1

Below is a graph for this function, where you can see the cut points with the axes, the vertex and axis of symmetry